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首页> 外文期刊>Journal of Mathematical Biology >Nonlinear studies of tumor morphological stability using a two-fluid flow model
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Nonlinear studies of tumor morphological stability using a two-fluid flow model

机译：双流体流动模型肿瘤形态稳定性的非线性研究

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We consider the nonlinear dynamics of an avascular tumor at the tissue scale using a two-fluid flow Stokes model, where the viscosity of the tumor and host microenvironment may be different. The viscosities reflect the combined properties of cell and extracellular matrix mixtures. We perform a linear morphological stability analysis of the tumors, and we investigate the role of nonlinearity using boundary-integral simulations in two dimensions. The tumor is non-necrotic, although cell death may occur through apoptosis. We demonstrate that tumor evolution is regulated by a reduced set of nondimensional parameters that characterize apoptosis, cell-cell/cell-extracellular matrix adhesion, vascularization and the ratio of tumor and host viscosities. A novel reformulation of the equations enables the use of standard boundary integral techniques to solve the equations numerically. Nonlinear simulation results are consistent with linear predictions for nearly circular tumors. As perturbations develop and grow, the linear and nonlinear results deviate and linear theory tends to underpredict the growth of perturbations. Simulations reveal two basic types of tumor shapes, depending on the viscosities of the tumor and microenvironment. When the tumor is more viscous than its environment, the tumors tend to develop invasive fingers and a branched-like structure. As the relative ratio of the tumor and host viscosities decreases, the tumors tend to grow with a more compact shape and develop complex invaginations of healthy regions that may become encapsulated in the tumor interior. Although our model utilizes a simplified description of the tumor and host biomechanics, our results are consistent with experiments in a variety of tumor types that suggest that there is a positive correlation between tumor stiffness and tumor aggressiveness.
机译：我们考虑使用双流体流动斯托克斯模型在组织规模处考虑缺血肿瘤的非线性动力学，其中肿瘤和宿主微环境的粘度可能是不同的。粘度反映了细胞和细胞外基质混合物的组合性质。我们对肿瘤进行线性形态稳定性分析，我们使用两个维度的边界整体模拟来研究非线性的作用。肿瘤是非坏死的，尽管通过细胞凋亡可能发生细胞死亡。我们证明肿瘤进化是通过表征细胞凋亡，细胞 - 细胞/细胞 - 细胞外基质粘附，血管化和肿瘤和宿主粘度的比例的减少的非潜能参数来调节。该方程的新型重构使得能够使用标准边界积分技术来数控求解方程。非线性模拟结果与几乎圆形肿瘤的线性预测一致。随着扰动发展和生长，线性和非线性结果偏离和线性理论倾向于扰动扰动的生长。仿真揭示了两种基本类型的肿瘤形状，具体取决于肿瘤和微环境的粘度。当肿瘤比其环境粘稠时，肿瘤倾向于开发侵入式手指和分枝状结构。随着肿瘤和宿主粘度的相对比降低，肿瘤倾向于以更紧凑的形状生长，并在肿瘤内部中封装的健康区域的复杂地区产生复杂的侵略性。虽然我们的模型利用肿瘤和宿主生物力学的简化描述，但我们的结果与各种肿瘤类型的实验一致，表明肿瘤僵硬和肿瘤侵袭性之间存在正相关性。

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